Formative and Summative Assessments

Currently, I am working on a unit on decimals.  I know that I will be teaching sixth-graders how to add, subtract, multiply, and divide multi-digit decimals. Since these are my teaching objectives, I now must develop ways to test my students during and at the end of this unit.

I can give my students an assessment that doesn’t count for much (if any) of their grade, just to see if they are understanding how to apply basic arithmetic operations to decimals.  Such an assessment is known as a formative assessment.  An example of a formative assessment for multiplication of decimals is a multiple choice quiz that only focuses on placing the decimal in the right place in the answer.  If I make the assessment reflect a real-world activity that involves the addition and multiplication of decimals then it would qualify as a performance-based formative assessment.  I think it would be fun to assign my sixth-graders the task of pricing three gift items for a baby shower, a birthday party, or Mother’s/Father’s Day.  Students would take photos of the items and their prices, total the prices, and then multiply the sum by the decimal .07 to calculate the sales tax.  Students would make a poster, powerpoint or document showing the photos, the sum of the prices, the sales tax, and the final total.

Again, this assessment is only formative since it only involves addition and multiplication rather than all four operations.  It cannot be used as a unit test.  Tests that assess the mastery of math skills and count toward the student’s grade would be classified as a summative assessment.  An example of a 20 problem summative test for this unit includes five problems for each operation involving multi-digit decimals.  Now that I have these assessments, I am better prepared to develop lessons on decimals.

What I’ve Learned About Unpacking Standards and Backward Planning

I am extremely grateful for the TEACH-NOW teacher certification program.  In just a few months I have learned more than I dreamed I would.  Each week is a new adventure.  This week I learned about unpacking a standard and backward mapping.  Wow!

I teach at a private school whose curriculum is not aligned with Common Core standards.  Before I began the TEACH-NOW program, I became familiar with the Georgia Department of Education State Standards for Middle School Math. Honestly, I read them but they didn’t mean much to me.  However, now that TEACH-NOW has explained it to me, unpacking the meaning of a standard is quite easy.  A standard states something a student is expected to be able to do.

This standard has the following verbs: add, subtract, multiply, and divide.  The object of all this action is the noun phrase “multi-digit decimals.”  I now understand this standard. It needs at least four main lessons (one for each verb) designed to impart the four skills that will be assessed. For a fuller example of unpacking standards, see my video.

A standard is an example of backward planning.  The standard is the goal that the teacher is pursuing for the students.  Exams or projects will be used to demonstrate that the appropriate skills have been developed.  The lessons and activities will help the students master the skills delineated by the standard.  Standards are simple and powerful.  For a fuller example of the Backward Planning process, see my previous blog.

What was I doing before I learned about unpacking standards and backward planning?  I was lesson-focused.  What lesson does the textbook say to teach next?  What kind of problems does the textbook use?  Based on the answers to these questions, I would teach the next lesson and make quizzes and tests like the textbook problems.

This approach isn’t bad, but it has a potential downside.  The teacher may be unaware of the bigger picture (of sixth-grade math, for example) and may be teaching disjointed, seemingly unrelated lessons.  State standards offer the teacher a map of concepts that a teacher can build lessons around. Yet, as far as I can tell, the state of Georgia has established a sixth-grade math curriculum that has planned every aspect of every lesson for every standard.  Potentially, a teacher could be once again lesson-focused.  However, the lessons always start with a list of state standards to which the wise teacher would do well to pay attention.  With the goal (standard) firmly in mind, the teacher is more likely to help the student reach it.

Now that I understand unpacking standards and backward planning, I feel less like a glorified substitute teacher and more like a professional teacher.  I have a long way to go, but I’m on my way!

Moving Toward Lesson Planning Using Backward Mapping

I am still learning the ropes of teaching.  I usually start with my textbooks, formulate lessons, and then design assessments.  This is a blog on a better practice for creating lessons.

That better way to plan a lesson is to start with the end result in mind, a method known as backward mapping.. “Backward design, also called backward planning or backward mapping, is a process that educators use to design learning experiences and instructional techniques to achieve specific learning goals. Backward design begins with the objectives of a unit or course—what students are expected to learn and be able to do—and then proceeds ‘backward’ to create lessons that achieve those desired goals” (Backward Design Definition, 2013).

The first standard on which I am using this method is a Georgia State Standard for sixth-grade math. It is as follows:

It is easy to find the proficiencies this standard is designed around: adding, subtracting, multiplying, and dividing decimals.  I will focus on three of these.

These proficiencies represent the ends that I am beginning with, the destinations I am seeking my students to reach.  I will know they have reached these goals if they pass assessments of these skills.  Two of my assessments are standard math tests.  The first will test the first two proficiencies, Add/Subtract Decimals Test, and the second will test the third proficiency, Multiplying Decimals Test.  The third assessment will test students ability to recall the rules associated with adding, subtracting, and multiplying decimals.  For example, to add and subtract decimals you must align numbers by their decimals.  To multiply decimals does not require decimal alignment, but instead one must count the total number of decimal places used in the problem and give the answer the same amount of decimal places.  Students will express these rules and give sample problems through one of the following media: a video, a song/poem, or poster.  Here is an example:

Having determined my standard, proficiencies, and assessments, I am ready to create my learning experiences that will move my students toward the goals.

1. Adding Decimals Lesson Outline
1. Whiteboard Lecture
1. Rules for Adding Multi-Digit Decimals
2. Demonstration of Algorithm for Adding Decimals
2. Mini-Whiteboard Challenge: students compete to get the right answer to 20 problems on their mini-white boards.
3. Homework: 10-problem worksheet and making 10 copies of the rules for adding decimals
2. Subtracting Decimals Lesson Outline
1. Video Lesson and Demonstration of Algorithm for Subtracting Decimals
2. Worksheet with 30 problems
3. Homework: None
3. Multiplying Decimals Lesson Outline
1. Whiteboard Lecture
1. Rules for Multiplying Multi-Digit Decimals
2. Demonstration of Algorithm for Multiplying Decimals
2. Large and mini-whiteboard challenge: All students work 12 problems, most on mini-whiteboards while taking turns solving problems on the main whiteboard.
3. Homework: 10-problem worksheet and making 10 copies of the rules for multiplying decimals

Backward planning makes sense.  I look forward to developing these lessons further and implementing them this semester.

Reference

Backward Design Definition. (2013, December 13). Retrieved September 12, 2017, from http://edglossary.org/backward-design/